Ruiyuan Chen

collaborators

3 papers

math.LO2025

Optimal Syntactic Definitions of Back-and-Forth Types

Ruiyuan Chen, David Gonzalez, Matthew Harrison-Trainor

The back-and-forth relations $M \leq_{I^} \pm N$ are central to computable structure theory and countable model theory. It is well-known that the relation ${(M, N) : M \leq_{I^} \pm N}$ is (ligh…

math.CT2025

Hilbert spaces admit no finitary discrete imaginaries

Ruiyuan Chen, Isabel Trindade

We prove that every functor from the category of Hilbert spaces and linear isometric embeddings to the category of sets which preserves directed colimits must be essentially consta…

math.LO2025

Componentwise Polish groupoids and equivalence relations

Ruiyuan Chen

We study Borel equivalence relations equipped with a uniformly Borel family of Polish topologies on each equivalence class, and more generally, standard Borel groupoids equipped wi…